9.3 Transform Graphs of Linear Functions Use this blank page to compile the most important things you want to remember for cycle 9.

Transcription

1 9. Transorm Graphs o Linear Functions Use this blank page to compile the most important things you want to remember or cycle 9.: Sec Math In-Sync by Jordan School District, Utah is licensed under a 6

2 Function Transormation Transormations o Functions It is diicult to see the eects o transormations on linear and eponential unctions, ecept or the vertical shit. Eamples: In the eamples below, k = or k = -. The original unctions are shown irst. In subsequent graphs, the original graphs are dashed. Original Function: Original Function: g The transormation k or g k is a vertical translation. Notice that i k is positive, the graph will shit up. I k is negative, then the graph will shit down. The output o the unction is being changed i.e. or g increased by, hence the downward and upward translation it s decreased by and or respectively. g Sec Math In-Sync by Jordan School District, Utah is licensed under a 64

3 The transormation k or kg is a vertical stretch or compression. I k is negative, the graph will be relected over the -ais. This transormation is very diicult to see with linear and eponential unctions unless looking at a relection with an eponential unction. Again, the output o the unction is being transormed i.e., the output is being multiplied by something, hence compressing, stretching, or relecting the output. 6 g The transormation k or g k is a horizontal stretch or compression. I k is negative, the graph will be relected over the y-ais. Again, the eects o this transormation are not easy to see with linear and eponential unctions. A relection over the y-ais with an eponential unction is more apparent. 6 g( ) The transormation k or g k, is a horizontal translation. Notice that i k is positive, the graph will shit to the let. I k is negative, then the graph will shit to the right. Again, the input o the unction is aected. ( ) 5 g ( ) Sec Math In-Sync by Jordan School District, Utah is licensed under a 65

4 9.a (build) Vertical Transormations Given the unction, perorm the ollowing transormations. Write the new equation and graph it on the graph provided. Be sure to label your new unction on the graph.. g g =. h h =. j h j = Indicate the transormation done to in order to obtain the ollowing equations. 7. g 5 8. h 9. j 5 Given the unction, perorm the ollowing transormations. Write the new equation. Graph it on the graph provided. Label your new unction on the graph.. g( ) ( ) 5. h( ) ( ) 5. j( ) h( ) 5 g = h = j = Indicate the transormation done to in order to obtain the ollowing equations. 6. g 7. h 8. j For each unction below write an equation rom the verbal description i and g 4 9. shit up 4. shit g down. shit g up. Shit down. Sec Math In-Sync by Jordan School District, Utah is licensed under a 66

5 . For large parties, a restaurant requires a reservation ee o $5, plus a $5 charge per person. The total charge or a party o people is 5 5. a) How will the graph o this unction change i the reservation ee is raised to $5? b) How will the graph change i the charge per person is lowered to $? 4. A lorist charges $5 or a vase, plus $4.5 or each lower. The total charge or the vase and lowers is given by the unction a) How will the graph change i the cost o the vase is raised to $5? b) How will the graph change i the charge per lower is lowered to $.? 5. A book club charges a membership ee o $ and then $ or each book purchased. a) Let y equal the total cost o membership in the club based on the number o books purchased. b) Write a second unction to represent the total cost o membership i the club raises its membership ee to $. c) Describe the relationship between the two unctions. 6. Kelly works as a salesperson. She earns a weekly base salary, plus a commission that is a percentage o her total sales. Her total weekly pay is described by., where is the total in sales dollars. a) What is Kelly s weekly base salary? b) What percentage o the total sales does Kelly receive as commission? c) What is the change in Kelly s salary plan i the weekly pay unction changes to g.5 d) What is the change i the unction is h. 4?? Sec Math In-Sync by Jordan School District, Utah is licensed under a 67

6 9.b (build) Horizontal and Vertical Linear EquationTransormations Part A: Vertical and Horizontal Shits. Begin with translations o linear equations. Think about slope intercept orm ( y m b), slope, and intercepts. Compare the unctions below to. a. b. 6 c. 5. Graph the unctions in # above. Use colored pencils. Label the lines. a. What part o the equation (y = m+b) did we change? b. What did this transormation do to the graph? c. Eplain why we call this a vertical translation transormation. Part B: Vertical shits and equations. Graph the equation 4. Label it. Write a contet or the unction. a. Move up. Sketch. Label this unction g =. Modiy the contet or the new unction. b. Move line down. Sketch. Label this unction r =. Modiy the contet or the new unction. c. Move line g up. Sketch. Label this unction v. Modiy the contet or the new unction. 4. What is the relationship o the unctions, g, r, and v? 5. To deine the vertical translation transormation o, we write k, where k is deining the vertical shit. Fill in the blanks or the ollowing: I k is the graph is translated up, and i k is the graph is translated down. Sec Math In-Sync by Jordan School District, Utah is licensed under a 68

7 Part C: Horizontal shits and equations 6. Graph and label. a. Graph and label. Describe the transormation. b. Graph and label. Describe the transormation. c. Graph and label. Describe the transormation. d. Graph and label. Describe the transormation. 7. How is changing in each equation? 8. How does it aect the graph o? What happened to the -intercept? 9. To deine the horizontal transormation o, we write k, where k is deining the horizontal shit. Fill in the blanks or the ollowing: I k is the graph is translated, and i k is the graph is translated.. I, what is the dierence in the transormations o and Part D: Practice Vertical and horizontal shits?. For each unction below, write an equation or the transormation described i. A vertical slide down 4.. A vertical slide down. 5. A vertical slide up A horizontal slide to the let. Indicate the transormation done to. A horizontal slide to the right. 4. A vertical slide up and a horizontal slide to the let A vertical slide down 5 and a horizontal slide to the right. given by the equation Sec Math In-Sync by Jordan School District, Utah is licensed under a 69

8 9.c (reine) Linear Vertical and Horizontal Transormation Practice Given:. Sketch. a. Sketch the unction y given by the transormations to below in 4. b. Write the new equation or each transormation. y.. y. y y 4. 4 Graph and g. Describe the transormation rom the graph o, g 4 5., g , g 8. g, 4 to the graph o g. Describe the transormation(s) on the graph o 4 that result in the graph o g. g g 4. g 4 5. g 4 Given the ollowing transormations, rewrite the equation o. Translate up units and to the let. 4. Translate to the right 4 units. 5. Translate down units and to the let 6 units. 6. Translate to the let 8 units. 7. You have seen that the graph o g is the result o translating the graph o three units up. However, you can also think o this as a horizontal translation that is, a translation let or right. Graph g to get the graph o. g. Describe the horizontal translation o the graph o Sec Math In-Sync by Jordan School District, Utah is licensed under a 7

9 9.d HONORS (reine) Transormations Shits The unction () is graphed. It has a domain o [-, 5] or 5 and a range o [-, 4] or y y 4. Perorm the indicated transormations. Then ind the domain and range o the new unction and describe the transormation. Vertical Shits A. Graph B. Graph Horizontal Shits A. Graph B. Graph Vertical Stretch (or Shrink)(s) A. Graph B. Graph Sec Math In-Sync by Jordan School District, Utah is licensed under a 7

10 Horizontal Stretch (or Shrink) A. Graph B. Graph Relection over the -ais or y-ais A. Graph B. Graph Combining Transormations A. Graph B. Graph Doing Transormations rom a Verbal Description Write the transormation, graph and identiy the domain and range. A. Shited down two and to the right one. B. Graph moved to the let and has a vertical stretch o. C. Graph has a horizontal stretch o one hal and then moved up one. Sec Math In-Sync by Jordan School District, Utah is licensed under a 7

11 9.e HONORS (apply) Transormation Shit Practice Given the graph, table, and domain and range o () below: a. Complete the tables b. Sketch the resulting graph c. Record the new domain and range () - Domain:, - - Range:,. y ( ). y ( ). y ( ) 4. y ( ) 5. y ( ) - - y 7. y ( ) - - y 9. y y () Given the graph above or (), write the equation, graph the new unction, and indicate the domain and range or the ollowing:. Moved to the let and down.. Vertical stretch o and moved up.. Relection over the -ais and moved to the right. - - Sec Math In-Sync by Jordan School District, Utah is licensed under a 7